Context. There are typically two different approaches to infer the mass formation history (MFH) of a given galaxy from its luminosity in different bands. Non-parametric methods are known for their flexibility and accuracy, while parametric models are more computationally efficient. Aims. In this work we propose an alternative that combines the advantages of both techniques, based on a polynomial expansion around the present time. Methods. In our approach, the MFH is decomposed through an orthonormal basis of N polynomia in lookback time. To test the proposed framework, synthetic observations are generated from models based on common analytical approximations (exponential, delayed-tau and Gaussian star formation histories). A normalized distance is used to measure the quality of the fit, and the input MFH are compared with the polynomial reconstructions both at the present time as well as through cosmic evolution. Results. The observed luminosities are reproduced with an accuracy of around 10 per cent for a constant star formation rate (N=1) and better for higher-order polynomia. Our method provides good results on the reconstruction of the total stellar mass, star formation rate and even its first derivative for smooth star formation histories, but it has difficulties in reproducing variations on short timescales and/or star formation histories peaking at the earliest times of the Universe. Conclusions. The polynomial expansion appears to be a promising alternative to other analytical functions used in parametric methods, combining both speed and flexibility.
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